SEARCH · Engineering Papers

Results for “density”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,189 records · Page 66

All sources NASA NTRS DOE OSTI

NASA NTRS2018

Rayleigh Scattering Density Measurements from Ultrafast Lasers in High-Pressure, Cryogenic Wind Tunnels

The Rayleigh scattering signal from femtosecond laser pulses is examined for its utility at making instantaneous density measurements in the NASA Langley 0.3-m Transonic Cryogenic Tunnel. An electron-multiplying CCD camera is used to visualize Rayleigh scattering signal taken concurrently with velocity measurements utilizing the femtosecond laser tagging velocimetry technique (FLEET). The results indicate a strong potential for making instantaneous measurements. Viable single-shot images are obtained over the full operational envelope of the facility, and shot-to-shot variations are found to be on average 6 percent (at 95 percent confidence level) and tend to decrease as the facility density is increased. The Rayleigh scattering signals observed before the optical focus exhibit a characteristically linear dependence on the mass-density of the gas, while signals after the focus exhibit a nonlinear (sublinear) density dependence, indicative of stronger absorption at higher densities. The measured Rayleigh scattering signals compare favorably to theoretical assessments made at the tunnel operating conditions.

Burns, Ross A.↗

NASA NTRS2018

Saturn's Plasma Density Depletions Along Magnetic Field Lines Connected to the Main Rings

We report on a set of clear and abrupt decreases in the high-frequency boundary of whistlerode emissions detected by Cassini at high latitudes (about ±40°) during the low-altitude proximal flybys f Saturn . These abrupt decreases or dropouts have start and stop locations that correspond to L shells at the dges of the A and B rings. Langmuir probe measurements can confirm, in some cases, that the abrupt decrease in the high-frequency whistler mode boundary is associated with a corresponding abrupt electron density dropout over evacuated field lines connected to the A and B rings. Wideband data also reveal electron plasma oscillations and whistler mode cutoffs consistent with a low-density plasma in the region. he observation of the electron density dropout along ring-connecting field lines suggests that strong ambipolar forces are operating, drawing cold ionospheric ions outward to fill the flux tubes. There is an analog with the refilling of flux tubes in the terrestrial plasmasphere. We suggest that the ring-connected electron density dropouts observed between 1.1 and 1.3 R(sub s) are connected to the low-density ring plasma cavity observed overtop the A and B rings during the 2004 Saturn orbital insertion pass.

Farrell, W. M.↗

NASA NTRS2020

Exploratory Experiments to Probe the Effect of Bulk Density and Porosity on The Morphology and Ejecta Kinematics of Impact Craters

The morphometry of relatively small impact craters are influenced by the physical properties of the target. To investigate the control of bulk density and porosity on the crater-formation processing the gravity regime, we conducted a series of impact experiments, varying each these target parameters while holding the other constant. Three different sands were used to construct cohesionless targets: quartz (0.4-0.8 mm), garnet (0.425-1.0 mm), and alumina (0.297-0.71mm), representing a range of intrinsic grain densities from 2.65 to 4.02 g cm-3. High-porosity targets were constructed by carefully pouring the sand into the center of a cylindrical PVC target bucket (inner diameter 26.2 cm, height 12 cm) and allowing it to fill the bucket at the angle of repose before being leveled flat at the top of the bucket. Low-porosity targets were obtained by pluviation of the granular material through a 1 mm sieve that was set directly above the target bucket. With the disparate intrinsic densities of the sand in combination with the variations of the packing technique, we attained differences in the bulk-target density of up to 32%while keeping porosity constant. The impact experiments were conducted with the vertical gun in the Experimental Impact Laboratory at NASA Johnson Space Center; using 3/16” (4.76 mm) diameter aluminum projectiles launched at1.55 ± 0.03 km s-1. The ejecta were observed using the laser-based Ejection Velocity Measurement System, providing data on launch positions and velocities of ejected particles. Submillimeter topographic data of the resulting craters were collected after each experiment with a NextEngine 3D scanner. Regardless of target material or density, all craters exhibited a simple bowl shape, but a trend of increasing depth-diameter ratio with increasing target porosity is observed across the entire experimental suite. Despite these morphometric differences, ejecta launch angles and speeds remain remarkably similar amongst all of the target configurations.

impact cratering↗

NASA NTRS2021

Photoionization Models for High Density Gas

Relativistically broadened and redshifted 6.4 – 6.9 keV iron K lines are observed from many accretion powered objects, including X-ray binaries and active galactic nuclei(AGN). Existence of gas close to the central engine implies large radiation intensities and correspondingly large gas densities if the gas is to remain partially ionized. Simple estimates indicate that high gas densities are needed to allow survival of iron against ionization. These are high enough that rates for many atomic processes are affected by mechanisms related to interactions with nearby ions and electrons. Radiation intensities are high enough that stimulated processes can be important. Most models currently in use for interpreting relativistic lines use atomic rate coefficients designed for use at low densities and neglect stimulated processes. In our work so far we have presented atomic structure calculations with the goal of providing physically appropriate models at densities consistent with line-emitting gas near compact objects. In this paper we apply these rates to photoionization calculations, and produce ionization balance curves and X-ray emissivities and opacities which are appropriate for high densities and high radiation intensities. The final step in our program will be presented in a subsequent paper: Model atmosphere calculations which incorporate these rates into synthetic spectra.

T Kallman↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8M⊕ with Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete dataset, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler -105 c has a radius of 1.3R⊕ and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 cimply an extremely low density of 0.1 g cm−3. In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Stars individual↗

NASA NTRS2022

Quantifying Feedback from Narrow Line Region Outflows in Nearby Active Galaxies. IV. The Effects of Different Density Estimates on the Ionized Gas Masses and Outflow Rates

Active galactic nuclei (AGN) can launch outflows of ionized gas that may influence galaxy evolution, and quantifying their full impact requires spatially resolved measurements of the gas masses, velocities, and radial extents. We previously reported these quantities for the ionized narrow-line region outflows in six low-redshift AGN, where the gas velocities and extents were determined from Hubble Space Telescope long-slit spectroscopy. However, calculating the gas masses required multicomponent photoionization models to account for radial variations in the gas densities, which span ∼6 orders of magnitude. To simplify this method for larger samples with less spectral coverage, we compare these gas masses with those calculated from techniques in the literature. First, we use a recombination equation with three different estimates for the radial density profiles. These include constant densities, those derived from [S ii], and power-law profiles based on constant values of the ionization parameter (U). Second, we use single-component photoionization models with power-law density profiles based on constant U, and allow U to vary with radius based on the [O iii]/Hβ ratios. We find that assuming a constant density of nH = 10(^2) cm(^−3) overestimates the gas masses for all six outflows, particularly at small radii where the outflow rates peak. The use of [S ii] marginally matches the total gas masses, but also overestimates at small radii. Overall, single-component photoionization models where U varies with radius are able to best match the gas mass and outflow rate profiles when there are insufficient emission lines to construct detailed models.

Mitchell Revalski↗

NASA NTRS2022

Terrestrial Exospheric Dayside H-density Profile at 3 - 15 RE from UVIS/HDAC and TWINS Lyman-alpha Data Combined

Terrestrial ecliptic dayside observations of the exospheric Lyman-α column intensity between 3–15 Earth radii (RE) by UVIS/HDAC (UVIS – ultraviolet imaging spectrograph; HDAC – hydrogen-deuterium absorption cell) Lyman-α photometer at CASSINI have been analyzed to derive the neutral exospheric H-density profile at the Earth’s ecliptic dayside in this radial range. The data were measured during CASSINI’s swing-by maneuver at the Earth on 18 August 1999 and are published by Werner et al. (2004). In this study the dayside HDAC Lyman-α observations published by Werner et al. (2004) are compared to calculated Lyman-α intensities based on the 3D H-density model derived from TWINS (Two Wide-angle Imaging Neutral-atom Spectrometers) Lyman-α observations between 2008–2010 (Zoennchen et al., 2015). It was found that both Lyman-α profiles show a very similar radial dependence in particular between 3–8RE. Between 3.0–5.5RE impact distance Lyman-α observations of both TWINS and UVIS/HDAC exist at the ecliptic dayside. In this overlapping region the cross-calibration of the HDAC profile against the calculated TWINS profile was done, assuming that the exosphere there was similar for both due to comparable space weather conditions. As a result of the cross-calibration the conversion factor between counts per second and rayleigh, fc = 3.285 counts s−1R−1, is determined for these HDAC observations. Using this factor, the radial H-density profile for the Earth’s ecliptic dayside was derived from the UVIS/HDAC observations, which constrained the neutral H density there at 10RE to a value of 35 cm-3. Furthermore, a faster radial H-density decrease was found at distances above 8RE (≈r−2.37) compared to the lower distances of 3–7RE (≈r−2.37). This increased loss of neutral H above 8RE might indicate a higher rate of H ionization in the vicinity of the magnetopause at 9–11RE (near subsolar point) and beyond, because of increasing charge exchange interactions of exospheric H atoms with solar wind ions outside the magnetosphere.

Jochen H Zoennchen↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8 M⊕ With Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete data set, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler-105 c has a radius of 1.3 R(sub ⨁) and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 c imply an extremely low density of ∽0.1 g cm(exp −3). In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Individual stars↗

NASA NTRSDate not supplied

High Density Vertiplex: Scalable Autonomous Operations Prototype Assessment Simulation

Urban Air Mobility is a rapidly growing topic within the field of aviation because of the impact a refined ecosystem and uncrewed aerial vehicles could have on modern society, such as urban air, cargo, and emergency transport. Before the UAM concept can be actualized, research is needed to understand how to integrate these new classes of vehicles and operations into the National Airspace System. One under-researched but critical piece of infrastructure required for UAM operations is Vertiport operations. Vertiports are the envisioned takeoff and landing locations for these uncrewed aerial vehicles. To accommodate the high use of the vertiport, new technologies and roles will be required for optimal use. At NASA, the High Density Vertiplex sub-project targets research into vertiports. The High Density Vertiplex team created their own Advanced Air Mobility ecosystem to test and evaluate different concepts and tools used to support higher density operations at vertiports. Part of the test and evaluation included the Prototype Assessment Operations simulation of high-density operations around a vertiport to study vertiport management and vertiport operations. The research team also evaluated how their simulated Urban Air Mobility ecosystem supported fleet managers, ground control station operators, and vertiport managers in execution of nominal and off-nominal high-density operations. Takeaways from this simulation helped the team evaluate well how the users of the ecosystem were able to use the components of the ecosystem to complete Urban Air Mobility missions.

Small Uncrewed Aerial Vehicle (sUAS)↗

NASA NTRS2024

Designing Lightweight Neutron Absorbing Composites Using a Comprehensive Absorber Areal Density Metric

Efforts to lightweight neutron absorbing composites are limited by incomplete understandings of the interaction between absorbing particles and their matrices. In this study, analytical models and a more physically representative simulation evaluated the penalty to neutron absorbing performance due to neutron channeling between large absorbing particles. Models and simulation agreed that B 4 C particles smaller than 100μm and especially those smaller than 10μm did not cause excessive neutron channeling. A more comprehensive neutron absorbing composite design metric – boron-10 equivalent areal density, which considers the particle size penalty and the matrix contribution to absorptivity – was introduced and used to estimate lightweighting via matrix substitution. Calculations using this new metric showed that a non-absorbing Mg matrix reduced mass by up to 35% over Al, constrained by the difference in mass density, while an absorbing Mg–Li matrix reduced mass by up to 60%, exceeding the difference in mass densities alone. Measurement of apparent absorber areal density through two experimental techniques – foil activation and direct counting – validated estimated absorber areal density as a neutron absorbing composite design metric. This updated understanding of the particle size penalty, newly introduced design metric, and experimental validation demonstrate a path to lightweight neutron absorbing composites.

Radiation shielding↗

DOE OSTI2018

Application of a Triple Bubbler Sensor for Determining the Density, Surface Tension, and Depth in Molten Salts

Electrochemical (i.e. pyroprocessing) technology is being widely studied throughout the world as a potential alternative to aqueous reprocessing of spent nuclear fuel (SNF). Central to this process is the electrorefiner (ER), in which the useful uranium in the SNF is electrochemically transported through a molten salt electrolyte to a cathode for later recovery. As part of this process, uranium, plutonium, and other actinides accumulate in the ER salt over time. Material accountancy and safeguards of these special nuclear material buildups in near real-time is a significant challenge due to the elevated processing temperatures, remote operation within a hotcell, and high radiation fields. Analytical techniques outside of the hotcell can be used to provide the SNM concentrations of salt samples from the ER. However, determining the actual mass of these materials in the ER presents a significant challenge because the density and volume within the vessel is largely unknown. The Idaho National Laboratory (INL) has developed a triple bubbler sensor capable of determining the density, surface tension, and depth of a fluid in near real-time. Previous experiments in aqueous media has shown that the sensor is capable of determining the density, surface tension and depth with accuracies on the order of 0.2%. The goal of this current work is to test the sensor in several molten salt media to calibrate and validate the triple bubbler. Experiments have been performed in LiCl-KCl eutectic salt. Calibration factors were 1.0015 and 1.26 for density and surface tension, respectively. With the above calibration factors applied, the depth of the salt in the test vessel was determined to within 0.4%. These results indicate that the triple bubbler sensor has the potential to accurately (less than 1% uncertainty) determine the density, surface, tension, and depth of the ER salt in near real-time. The triple bubbler sensor designed at INL can significantly enhance the material accountancy, safeguards, and process monitoring of the electrochemical processing of SNF.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2019

Experimental Investigation of a Novel High Energy Density Mobile Sorption–based Thermal Battery

Around 20% of the total primary energy use in the United States is for thermal demands of buildings, such as space cooling, dehumidification, and space heating. Low-grade geothermal energy is abundant and could effectively satisfy these thermal demands. However, low-grade geothermal energy is underused because geothermal fluids have an energy density too low to justify transportation between the existing resources and buildings. The mobile sorption-based thermal battery (MSTB) system was thus developed to store the low-temperature heat using three-phase (vapor-liquid solution-solid crystal) sorption technology with a much higher energy density than a geothermal fluid provides. The energy density of an MSTB is over 6 times that of conventional hot water, enabling economical long-distance transport of low-temperature heat for thermal end uses. This can alleviate peak demand on the electricity grid by offsetting space-conditioning loads, improving the reliability and resilience of US energy systems. High energy density, fast crystallization, and crystal dissolution of the sorption material are critical to the viability and performance of the MSTB system. Therefore, the design and operation of MSTB systems must ensure effective generation and dissolution of the salt crystals inside the MSTB. To achieve this target, this study developed a prototype MSTB and its testing apparatus, and experimentally investigated the prototype MSTB. The crystallization and dissolution performance were also theoretically defined and quantified. The experimental results showed that the prototype MSTB was able to achieve an energy storage density of 903.0 kJ/kg and a maximum discharge rate of 1.3 kW. This study proves the feasibility and high performance of the MSTB concept, which is helpful to further study and development of the MSTB system.

Wang, Lingshi↗

DOE OSTI2017

A novel muon detector for borehole density tomography

Muons can be used to image the density of materials through which they pass, including geological structures. Subsurface applications of the technology include tracking fluid migration during injection or production, with increasing concern regarding such timely issues as induced seismicity or chemical leakage into aquifers. Current density monitoring options include gravimetric data collection and active or passive seismic surveys. One alternative, or complement, to these methods is the development of a muon detector that is sufficiently compact and robust for deployment in a borehole. Such a muon detector can enable imaging of density structure to monitor small changes in density – a proxy for fluid migration – at depths up to 1500 m. Such a detector has been developed, and Monte Carlo modeling methods applied to simulate the anticipated detector response. Testing and measurements using a prototype detector in the laboratory and shallow underground laboratory demonstrated robust response. Lastly, a satisfactory comparison with a large drift tube-based muon detector is also presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Wave induced density modification in RF sheaths and close to wave launchers

With the return to full metal walls - a necessary step towards viable fusion machines - and due to the high power densities of current-day ICRH (Ion Cyclotron Resonance Heating) or RF (radio frequency) antennas, there is ample renewed interest in exploring the reasons for wave-induced sputtering and formation of hot spots. Moreover, there is experimental evidence on various machines that RF waves influence the density profile close to the wave launchers so that waves indirectly influence their own coupling efficiency. The present study presents a return to first principles and describes the wave-particle interaction using a 2-time scale model involving the equation of motion, the continuity equation and the wave equation on each of the time scales. Through the changing density pattern, the fast time scale dynamics is affected by the slow time scale events. In turn, the slow time scale density and flows are modified by the presence of the RF waves through quasilinear terms. Although finite zero order flows are identified, the usual cold plasma dielectric tensor - ignoring such flows - is adopted as a first approximation to describe the wave response to the RF driver. The resulting set of equations is composed of linear and nonlinear equations and is tackled in 1D in the present paper. Whereas the former can be solved using standard numerical techniques, the latter require special handling. At the price of multiple iterations, a simple ’derivative switch-on’ procedure allows to reformulate the nonlinear problem as a sequence of linear problems. Analytical expressions allow a first crude assessment - revealing that the ponderomotive potential plays a role similar to that of the electrostatic potential arising from charge separation - but numerical implementation is required to get a feeling of the full dynamics. A few tentative examples are provided to illustrate the phenomena involved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Ionic liquid gating on atomic layer deposition passivated GaN: Ultra-high electron density induced high drain current and low contact resistance

Herein, we report on achieving ultra-high electron density (exceeding 10{sup 14 }cm{sup −2}) in a GaN bulk material device by ionic liquid gating, through the application of atomic layer deposition (ALD) of Al{sub 2}O{sub 3} to passivate the GaN surface. Output characteristics demonstrate a maximum drain current of 1.47 A/mm, the highest reported among all bulk GaN field-effect transistors, with an on/off ratio of 10{sup 5} at room temperature. An ultra-high electron density exceeding 10{sup 14 }cm{sup −2} accumulated at the surface is confirmed via Hall-effect measurement and transfer length measurement. In addition to the ultra-high electron density, we also observe a reduction of the contact resistance due to the narrowing of the Schottky barrier width on the contacts. Taking advantage of the ALD surface passivation and ionic liquid gating technique, this work provides a route to study the field-effect and carrier transport properties of conventional semiconductors in unprecedented ultra-high charge density regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Implementation of the new multichannel X-mode edge density profile reflectometer for the ICRF antenna on ASDEX Upgrade

A new multichannel frequency modulated continuous-wave reflectometry diagnostic has been successfully installed and commissioned on ASDEX Upgrade to measure the plasma edge electron density profile evolution in front of the Ion Cyclotron Range of Frequencies (ICRF) antenna. The design of the new three-strap ICRF antenna integrates ten pairs (sending and receiving) of microwave reflectometry antennas. The multichannel reflectometer can use three of these to measure the edge electron density profiles up to 2 × 10{sup 19} m{sup −3}, at different poloidal locations, allowing the direct study of the local plasma layers in front of the ICRF antenna. ICRF power coupling, operational effects, and poloidal variations of the plasma density profile can be consistently studied for the first time. In this work the diagnostic hardware architecture is described and the obtained density profile measurements were used to track outer radial plasma position and plasma shape.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Real-space formulation of the stress tensor for O (N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O (N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O (N) methods. We then describe its evaluation within the O (N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. In conclusion, we further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗